Very Basic Mathematical Latex

A document in the article style might be entered between the \maketitle and \end{document} sections below.

\documentclass{article}
%\addtolength{\textheight}{+ .1\textheight}
\title{TITLE}
\author{NAME}
%\date{}
\begin{document}

\maketitle

\end{document}

Paragraphs are separated by a blank line of input. Lines which start with % are viewed as having been commented out.

Most mathematical input is entered in ımath mode. Displayed formulas can be enclosed between \[ and \]; inline formulas between $ and $. A number of examples are given below. You can find long lists of mathematical symbols and accents at the web sites:

• http://www.agu.org/symbols.html

• http://www.giss.nasa.gov/latex/ltx-117.html

• http://omega.albany.edu:8008/Symbols.html

• http://www.lacim.uqam.ca/˜ zabrocki/LATEXmath/latexsym.html

Simple Constructions in Math Mode

Some Simple Displayed Formulas:

The character ˆ is for superscripts and is for subscripts. Single character subscripts don’t need to be enclosed in {}.

e^{iθ_{1}} = cos θ_{1} + i sin θ_{1}

e^{ i \theta_1} = \cos{\theta_1} + i \sin{\theta_1}

\frac{∂^{2}u}{∂x^{2}} = \frac{1}{c^{2}} \frac{∂^{2}u}{∂t^{2}}

\[
\frac{\partial^2 u}{\partial x^2}=
\frac{1}{c^2} \frac{\partial^2 u}{\partial t^2}
\]

Sometimes it is important not to leave a blank line before the \] ending a math mode display. Formulas can also be displayed inline by enclosing in $ signs; e.g. f(x) = \frac{d}{dx} ∫_{a}^{x} f(t) dt.

$f(x) =\frac{d}{dx} \int_a^x f(t) \ dt$

Matrices, Systems of Equations, Tables:

A Matrix

A = ( \begin{matrix}a & b \\ b & c \end{matrix} ) .

\[
A = \left(   \begin{array}{rr} a & b \\ b & c  \end{array}\right).
\]

The r’s indicate right justification. Alternatives are l or c.

A system of equations:

u cos (πu^{3}) + v + 1 = x
u + v^{2} cos (πv) + 1 = y

\begin{eqnarray*}
u\cos {(}\pi u^{3}{)}+v+1 &=&x \\
u+v^{2}\cos {(}\pi v{)}+1 &=&y
\end{eqnarray*}

A Simple Table:

T probability
2  \frac{1}{36}
3  \frac{2}{36}

\begin{table}[h]
\begin{center}
\begin{tabular}{r|c}
${\bf T}$& {\bf probability}\\ \hline
$2$ & $\frac{1}{36}$ \\
$3$ & $\frac{2}{36}$ \\
\end{tabular}
\end{center}
\end{table}

The vertical bars | and \hline commands control where horizontal and vertical lines appear in the table.

A Conditional Defintion

f(x, y) = \{ \begin{matrix}\frac{x^{2}y}{x^{4}+y^{2}} & if (x, y) ≠ (0, 0) \\ 0 & if (x, y) = (0, 0) \end{matrix}

\[
f(x,y)= \left\{ \begin{array}{ll}
 \frac{x^2y}{x^4+y^2} & \mbox{if $(x,y) \neq (0,0)$} \\
 0 & \mbox{if $(x,y) = (0,0)$} \\
   \end{array}
  \right. \\
\]

The \right. command closes the left delimiter \{ syntactically without displaying anything.

Lists

The itemize environment:

• item1

• item2

\begin{itemize}
  \item item1
  \item item2
\end{itemize}

The enumerate environment:

1. item1

2. item2

\begin{enumerate}
  \item item1
  \item item2
\end{enumerate}

The description environment:

a) item1

b) item2

\begin{description}
  \item[{\bf a) } ]  item1
  \item[{\bf b) } ]  item2
\end{description}

(The example above chooses to use boldface for the labels.)

Alignment, Font and Size Changes

Alignment

can be forced with • left: \noindent

• center: \begin{ center} … \end{ center}

• right: \begin{ flushright} … \end{ flushright}

• newline: \newline or \\

• newpage: \newpage

Text Size

You can change sizes by enclosing your text in brackets as in tiny: {\tiny … }. small: {\small … }. large: {\large … }. large: {\Large … }. large: {\LARGE … }.

Font Changes

are possible as in boldface: {\bf … }. italics: {\it … }.

Vertical Spacing

can be achieved by commands like \bigskip, \smallskip, or \vspace{5mm}.